Logistic (Sech-squared) Distribution

A special case of the Generalized Logistic distribution with $c=1$. The support is $x\in \mathbb{R}$.

This distribution function has a direct connection with the Fermi-Dirac distribution via its survival function. I.e. scipy.stats.logistic.sf is equivalent to the Fermi-Dirac distribution.

where ${\psi }_m$ is the polygamma function ${\psi }_m(z)=\frac{d^{m+1}}{d{z}^{m+1}}\log (\Gamma (z))$.

Implementation: scipy.stats.logistic